A150409 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (0, -1, 0), (0, 1, 0), (0, 1, 1), (1, 1, -1)}.

1, 2, 7, 24, 94, 370, 1532, 6430, 27613, 120105, 529004, 2353732, 10560201, 47741258, 217182975, 993689378, 4569028343, 21102587065, 97856367075, 455411592395, 2126424240714, 9958391469555, 46764973042169, 220162782395164, 1038904706385757, 4912935500411391, 23279408557702152, 110512017376178793

Offset

0,2

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150407 A317130 A150408 * A150410 A150411 A150412

Adjacent sequences: A150406 A150407 A150408 * A150410 A150411 A150412

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved